Addition and resolution of forces Adding forces Algebraic

Addition and resolution of forces

Adding forces Algebraic method The magnitude of the resultant force is the algebraic sum of the forces. Adding forces in the same direction & along the same line. F 1 F 2 F = F 1 + F 2 direction is the same as the forces Adding forces in the opposite direction & along the same line. F 1 F = F 1 - F 2 direction is the same as the larger force

1 Which of the following schoolbags would you feel heavier to carry if the same number of books are put in them? A B

2 A light rope is stretched tightly between two poles. A T-shirt of weight 8 N is hung at the midpoint of the rope. What is the tension T in the string? A T <4 N B T=4 N C T >4 N 8 N

Adding forces a Graphical method Force is a vector quantity. It has both magnitude and direction. Like displacements, forces can also be added graphically using the 'tip-to-tail' method. Lines representing forces should be drawn to scale.

Adding forces a Graphical method 'Tip-to-tail' method F 2 resultant force F 1 + F 2 F 1

Adding forces a Graphical method Parallelogram of forces method parallel F 2 F 1 + F 2 parallel F 1 resultant force

Addition of forces Stretch a rubber band with a spring balance. F 1 F B O A F 2 Stretch the rubber band by the same amount using 2 spring balances. Note the magnitude & direction of the F 1 & F 2. Check if resultant = F (in magnitude & direction) by –using 'tip-to-tail' method –using parallelogram of forces method

1 Adding forces c Algebraic method (2 -demensions) Forces in 2 dimensions can also be added algebraically. See this example:

Example 1 2 tug boats pull an oil rig, each exerting a force of 100 000 N, they are at 60 to each other. Find the resultant force.

Example 1 C Use 1 cm to represent 25 000 N Length of AC = 6. 9 cm Resultant = 6. 9 25 000 N = 173 000 N (with an of 30 to either force) resultant D B 100 000 N 60 A oil rig 100 000 N

Example 2 2 forces, 3 N and 4 N, act at right angles to each other. Find the magnitude & direction of the resultant force. =5 N 3 N R 5 N Resultant force is 5 N 4 N

If Janice is pushing with a force of 60 N & Tommy is pushing with 80 N, what are the maximum and the minimum magnitudes of their combined force? Maximum force Minimum force A 100 N 80 N B 120 N 60 N C 140 N 20 N D 160 N 40 N

Find the resultant of the forces below with graphical method. (1 cm represents 1. 5 N) 7 N The resultant force is ____ N 8. 9 43 making an angle _____ with the 3 -N force. 60° 3 N

2 ropes are used to pull a tree as shown. Find the magnitude of the resultant force acting on the tree. 120 N Magnitude of resultant 2 2 120 + = ______ (Pythagoras’ theorem) 170 = ____ N 120 N

Resolving forces into components a Graphical method Suppose a force F is represented by OC : y component Fy C Magnitudes of Fx & Fy can be measured directly. F component O Fx x

Resolving forces into components b Algebraic method Magnitudes of Fx & Fy can be also be found by algebraic method: y C (Pythagoras’ theorem) Fy F O F 2 = F x 2 + F y 2 Fx Fx = F cos Fy = F sin Fy tan = Fx x